Question

a solid cube is cut into 27 small cubes of equal volume find the ratio of the surface area of the given cube and that of one small cube

Answer 1

let the side of bigger cube be a
its volume a^3
no. of smaler cubes = 27
their volume = a^3/27
each side of smaller cube = (a^3/27)^1/3 = a/3
total surface area of bigger cube = 4×a^2=4a^2
total surface area of smaler cube=4(a/3)^2=4a^2/9
ratio of TSA of bigger cube to TSA of smaller cube = TSA of bigger cube/TSA of smaller cube
=4a^2÷4a^2/9
= 9 : 1
HOPE IT HELPS